How do you know if money is uncirculated?

"Uncirculated" simply means "never been spent and in change" so if you have a new coin or bill (banknote) from the bank or a cash machine, it's considered to be uncirculated. As soon as it's spent at a store or put in a vending machine it's been in circulation.

Of course if you have to prove that an item is uncirculated, that's more difficult. There are companies that get coins and bills directly from banks and resell them, and both the Mint (coins) and BEP (bills) will sell you uncirculated examples of their products. Then you know they're truly never circulated, but you'll have to pay extra for that assurance.